A parametric statistical postprocessing method is presented that transforms raw (and frequently biased) ensemble forecasts from the Global Ensemble Forecast System (GEFS) into reliable predictive probability distributions for precipitation accumulations. Exploratory analysis based on 12 years of reforecast data and ⅛° climatology-calibrated precipitation analyses shows that censored, shifted gamma distributions can well approximate the conditional distribution of observed precipitation accumulations given the ensemble forecasts. A nonhomogeneous regression model is set up to link the parameters of this distribution to ensemble statistics that summarize the mean and spread of predicted precipitation amounts within a certain neighborhood of the location of interest, and in addition the predicted mean of precipitable water. The proposed method is demonstrated with precipitation reforecasts over the conterminous United States using common metrics such as Brier skill scores and reliability diagrams. It yields probabilistic forecasts that are reliable, highly skillful, and sharper than the previously demonstrated analog procedure. In situations with limited predictability, increasing the size of the neighborhood within which ensemble forecasts are considered as predictors can further improve forecast skill. It is found, however, that even a parametric postprocessing approach crucially relies on the availability of a sufficiently large training dataset.

Statistical post-processing of dynamical forecast ensembles is an essential component of weather forecasting. In this article, we present a post-processing method which generates full predictive probability distributions for precipitation accumulations based on ensemble model output statistics (EMOS).We model precipitation amounts by a generalized extreme value distribution which is left-censored at zero. This distribution permits modelling precipitation on the original scale without prior transformation of the data. A closed form expression for its continuous ranked probability score can be derived and permits computationally efficient model fitting. We discuss an extension of our approach which incorporates further statistics characterizing the spatial variability of precipitation amounts in the vicinity of the location of interest.The proposed EMOS method is applied to daily 18 h forecasts of 6 h accumulated precipitation over Germany in 2011 using the COSMO-DE ensemble prediction system operated by the German Meteorological Service. It yields calibrated and sharp predictive distributions and compares favourably with extended logistic regression and Bayesian model averaging which are state-of-the-art approaches for precipitation post-processing. The incorporation of neighbourhood information further improves predictive performance and turns out to be a useful strategy to account for displacement errors of the dynamical forecasts in a probabilistic forecasting framework.

Proper scoring rules provide a theoretically principled framework for the quantitative assessment of the predictive performance of probabilistic forecasts. While a wide selection of such scoring rules for univariate quantities exists, there are only few scoring rules for multivariate quantities, and many of them require that forecasts are given in the form of a probability density function. The energy score, a multivariate generalization of the continuous ranked probability score, is the only commonly used score that is applicable in the important case of ensemble forecasts, where the multivariate predictive distribution is represented by a finite sample. Unfortunately, its ability to detect incorrectly specified correlations between the components of the multivariate quantity is somewhat limited. In this paper the authors present an alternative class of proper scoring rules based on the geostatistical concept of variograms. The sensitivity of these variogram-based scoring rules to incorrectly predicted means, variances, and correlations is studied in a number of examples with simulated observations and forecasts; they are shown to be distinctly more discriminative with respect to the correlation structure. This conclusion is confirmed in a case study with postprocessed wind speed forecasts at five wind park locations in Colorado.

The International Grand Global Ensemble (TIGGE) was a major component of The Observing System Research and Predictability Experiment (THORPEX) research program, whose aim is to accelerate improvements in forecasting high-impact weather. By providing ensemble prediction data from leading operational forecast centers, TIGGE has enhanced collaboration between the research and operational meteorological communities and enabled research studies on a wide range of topics. The paper covers the objective evaluation of the TIGGE data. For a range of forecast parameters, it is shown to be beneficial to combine ensembles from several data providers in a multimodel grand ensemble. Alternative methods to correct systematic errors, including the use of reforecast data, are also discussed. TIGGE data have been used for a range of research studies on predictability and dynamical processes. Tropical cyclones are the most destructive weather systems in the world and are a focus of multimodel ensemble research. Their extratropical transition also has a major impact on the skill of midlatitude forecasts. We also review how TIGGE has added to our understanding of the dynamics of extratropical cyclones and storm tracks. Although TIGGE is a research project, it has proved invaluable for the development of products for future operational forecasting. Examples include the forecasting of tropical cyclone tracks, heavy rainfall, strong winds, and flood prediction through coupling hydrological models to ensembles. Finally, the paper considers the legacy of TIGGE. We discuss the priorities and key issues in predictability and ensemble forecasting, including the new opportunities of convective-scale ensembles, links with ensemble data assimilation methods, and extension of the range of useful forecast skill.

This study applies statistical postprocessing to ensemble forecasts of near‐surface temperature, 24 h precipitation totals, and near‐surface wind speed from the global model of the European Centre for Medium‐Range Weather Forecasts (ECMWF). The main objective is to evaluate the evolution of the difference in skill between the raw ensemble and the postprocessed forecasts. Reliability and sharpness, and hence skill, of the former is expected to improve over time. Thus, the gain by postprocessing is expected to decrease. Based on ECMWF forecasts from January 2002 to March 2014 and corresponding observations from globally distributed stations, we generate postprocessed forecasts by ensemble model output statistics (EMOS) for each station and variable. Given the higher average skill of the postprocessed forecasts, we analyze the evolution of the difference in skill between raw ensemble and EMOS. This skill gap remains almost constant over time indicating that postprocessing will keep adding skill in the foreseeable future.

Hydrological forecasts strongly rely on predictions of precipitation amounts and temperature as meteorological forcings for hydrological models. Ensemble weather predictions provide a number of different scenarios that reflect the uncertainty about these meteorological inputs, but these are often biased and under‐dispersive, and therefore require statistical postprocessing. In addition to correcting the marginal distributions of the two weather variables, postprocessing methods must reconstruct their spatial, temporal, and intervariable dependence in order to generate physically realistic forecast trajectories that can be used as forcings of hydrological streamflow forecast models. For many years, a sample reordering method referred to as “Schaake shuffle” has been used successfully to address this multivariate aspect of forecast distributions by using historical observation trajectories as multivariate “dependence templates.” This paper proposes a variant of the Schaake shuffle, in which the historical dates are selected such that the marginal distributions of the corresponding observation trajectories are similar to the forecast marginal distributions, thus making it more likely that spatial and temporal gradients are preserved during the reordering procedure. This new approach is demonstrated with temperature and precipitation forecasts over four river basins in California, and it is shown to improve upon the standard Schaake shuffle both with respect to verification metrics applied to the forcings, and verification metrics applied to the resulting streamflow predictions.

Statistical postprocessing techniques are commonly used to improve the skill of ensembles of numerical weather forecasts. This paper considers spatial extensions of the well-established nonhomogeneous Gaussian regression (NGR) postprocessing technique for surface temperature and a recent modification thereof in which the local climatology is included in the regression model for a locally adaptive postprocessing. In a comparative study employing 21 h forecasts from the COSMO-DE ensemble predictive system over Germany, two approaches for modeling spatial forecast error correlations are considered: A parametric Gaussian random field model and the ensemble copula coupling approach which utilizes the spatial rank correlation structure of the raw ensemble. Additionally, the NGR methods are compared to both univariate and spatial versions of the ensemble Bayesian model averaging (BMA) postprocessing technique.

Interpolation of spatial data is a very general mathematical problem with various applications. In geostatistics, it is assumed that the underlying structure of the data is a stochastic process which leads to an interpolation procedure known as kriging. This method is mathematically equivalent to kernel interpolation, a method used in numerical analysis for the same problem, but derived under completely different modelling assumptions. In this article we present the two approaches and discuss their modelling assumptions, notions of optimality and the different concepts to quantify the interpolation accuracy. Their relation is much closer than has been appreciated so far, and even results on convergence rates of kernel interpolants can be translated to the geostatistical framework. We sketch the different answers obtained in the two fields concerning the issue of kernel misspecification, present some methods for kernel selection, and discuss the scope of these methods with a data example from the computer experiments literature.